diff --git a/pandas/core/apply.py b/pandas/core/apply.py
index 00b49c2f4f951..9ec0f7dca3b84 100644
--- a/pandas/core/apply.py
+++ b/pandas/core/apply.py
@@ -842,7 +842,7 @@ def apply_str(self) -> FrameOrSeriesUnion:
             # Special-cased because DataFrame.size returns a single scalar
             obj = self.obj
             value = obj.shape[self.axis]
-            return obj._constructor_sliced(value, index=self.agg_axis, name="size")
+            return obj._constructor_sliced(value, index=self.agg_axis)
         return super().apply_str()
 
 
diff --git a/pandas/tests/apply/test_frame_apply.py b/pandas/tests/apply/test_frame_apply.py
index 2511f6fc2563c..14266a2c29a7f 100644
--- a/pandas/tests/apply/test_frame_apply.py
+++ b/pandas/tests/apply/test_frame_apply.py
@@ -1279,9 +1279,9 @@ def test_size_as_str(how, axis):
     # on the columns
     result = getattr(df, how)("size", axis=axis)
     if axis == 0 or axis == "index":
-        expected = Series(df.shape[0], index=df.columns, name="size")
+        expected = Series(df.shape[0], index=df.columns)
     else:
-        expected = Series(df.shape[1], index=df.index, name="size")
+        expected = Series(df.shape[1], index=df.index)
     tm.assert_series_equal(result, expected)